REFRACTION OF I.IGIIT, REFRACTOMETRY AND INTERFEROMETRY 



Newton, who based upon such (evidence his 

 opinion that water and diamond must "con- 

 tain both some kind of combustible sub- 

 stance". Refractive indices, being affected 

 by many factors, are not additive. Therefore, 

 they are seldom used directly, although in 

 solutions of a single solute an empirical re- 

 lation linear with respect to concentration C : 



(n - no)/C = Cte (48)* 



is often usable. The refraction-density rela- 

 tionship of Newton: 



tivity, and a Lorencian formula in (n^ — 1) 

 when dealing with concentration and chemi- 

 cal effects; the reverse is more often correct, 

 however, when dealing with substances in 

 the glassy state. In either case, a simple 

 calculation can be used to find relative pro- 

 portions (by weight) of mixtures of nonpolar 

 substances in which insignificant volume 

 changes take place (most gases and many 

 very dilute solutions) : 



100(n - l)/d = bi(ni - 1)M] 



r, = (n2 - l)/d 



(49) 



+ [(100 - pi)(n2 - l)/d2] 



(52) 



(where d is the density) , although often suffi- 

 cient, is not general. J. H. Gladstone and I. 

 P. Dale (1858), and later Landolt (1864) 

 showed that another empirical relation is 

 much less dependent on temperature and 

 concentration changes : 



r,= (n- \)/d 



(50) 



This is known as the specific refractivity 

 (n — 1 being the refractivity) . A theoretical 

 derivation, made independently by Lorenz 

 (of Copenhagen) and Lorentz (of Leyden) in 

 1880 (118) is called the theoretical specific 

 refractivity or specific refraction: 



(or the corresponding (n^ — 1) quantities 

 for a "Newtonian" case, or (n^ — 1)/ 

 (n^ -j- 2) for a "Lorencian" case). If, in a 

 more general case, the volume variation c 

 is known and expressed by the relation: 



c = [(V, -i- V.) - V]/(v, + v.) (53) 



the relation may be further improved: 



[100(n - l)/d]-[(l - ac)/(l - c)] = 



[pi(n - l)/d.] + [(100 - pi)(7i2 - l)/d,\ 



(54) 



= (n^ - l)/(i(n2 + 2) 



(51) 



(the factor a usually varies with the wave- 

 length). 



Referring again to pure substances, the 

 empirical specific molar refractivity Mvg , 

 is given by: 



This relation is more general. It applies 

 regardless of the physical state of matter, 

 and it is valid at all wavelengths, although 

 a correction for spectral dispersion is re- 

 quired in each case. The constant 2 often 

 needs to be adjusted in particular cases. For 

 gases, particularly hydrocarbons, Eykman, 

 and also Gibson, (119) prefer the value 0.4. 

 Yet Zehnder and his associates found that a 

 factor of the form: (n — 1) in the above 

 formula followed more closely the experi- 

 mental data relative to the effect of pressure 

 on gases. A convenient rule — which is not 

 always valid — is to use a formula of the 

 (n — 1) form (Newtonian type) when dealing 

 with the effects of physical factors on refrac- 



* Equations 1-47 in preceding articles. 



Mrg = M(n - l)/d 



= M(n - l)-v = V(n - 1) 



(55) 



(where M is the molecular weight, v is the 

 specific volume and V is the molar volume: 

 V = Mv = M/d.) Similarly, one calculates a 

 molar refraction derived from the non-New- 

 tonian formula: 



Mrg* = M(n^ - l)/d(n'' + 2) 



= M(n'- - l)v/(n' + 2) 



(56) 



(and the variants mentioned above). It is 

 often more convenient to convert (56) to its 

 decimal log form: 



In Mrg* = In r/ + In M - In d (57) 

 (In is given directly in five-decimal log ta- 



516 



